pacman::p_load(tidyverse, funModeling, blorr, corrplot, ggpubr, sf,
spdep, GWmodel, tmap, skimr, caret, report)In-class_Exercise 5: Modeling the Spatial Variantion: the Explanatory Factors of Water Point Status using Geograhical Weighted Logistic Regression
Setting the scene
To build an explanatory model to discover factor affecting water point status in Osun State, Nigeria.
Study Area: Osun State, Nigeria
Data Sets:
Osun.rds contains LGA boundaries of Osun State. It is in sf polygon data frame.
Osun_wp_sf.rds: contains water points within Osun State. It is in sf point data frame.
Model Variables
Dependent variable: Water point status (i.e functional/non-functoinal)
Independent variables:
distance_to_primary_road,
distance_ to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
water_point_population,
local_population_km,
usage_capacity,
is_urban,
water_source_clean.
R packages
The code chunk below is used to load the packages to R environment.
The Data
The code chunk below is used to load the data to R environment.
Osun <- read_rds("rds/Osun.rds")
Osun_wp_sf <- read_rds("rds/Osun_wp_sf.rds")The code chunk below is used to show the frequency distribution of water point status.
True refers to Functional water points while False refers to non-functional water points.
Osun_wp_sf %>%
freq(input="status")Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
Please report the issue at <https://github.com/pablo14/funModeling/issues>.
status frequency percentage cumulative_perc
1 TRUE 2642 55.5 55.5
2 FALSE 2118 44.5 100.0tmap_mode("view")tmap mode set to interactive viewingtm_shape(Osun)+
tm_polygons(alpha = 0.4) +
tm_shape(Osun_wp_sf) +
tm_dots(col="status",
alpha = 0.6) +
tm_view(set.zoom.limits = c(9,12))Exploratory Data Analysis(EDA)
The code chunk below is used to do EDA for all variables.
Osun_wp_sf %>%
skim()Warning: Couldn't find skimmers for class: sfc_POINT, sfc; No user-defined `sfl`
provided. Falling back to `character`.| Name | Piped data |
| Number of rows | 4760 |
| Number of columns | 75 |
| _______________________ | |
| Column type frequency: | |
| character | 47 |
| logical | 5 |
| numeric | 23 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| source | 0 | 1.00 | 5 | 44 | 0 | 2 | 0 |
| report_date | 0 | 1.00 | 22 | 22 | 0 | 42 | 0 |
| status_id | 0 | 1.00 | 2 | 7 | 0 | 3 | 0 |
| water_source_clean | 0 | 1.00 | 8 | 22 | 0 | 3 | 0 |
| water_source_category | 0 | 1.00 | 4 | 6 | 0 | 2 | 0 |
| water_tech_clean | 24 | 0.99 | 9 | 23 | 0 | 3 | 0 |
| water_tech_category | 24 | 0.99 | 9 | 15 | 0 | 2 | 0 |
| facility_type | 0 | 1.00 | 8 | 8 | 0 | 1 | 0 |
| clean_country_name | 0 | 1.00 | 7 | 7 | 0 | 1 | 0 |
| clean_adm1 | 0 | 1.00 | 3 | 5 | 0 | 5 | 0 |
| clean_adm2 | 0 | 1.00 | 3 | 14 | 0 | 35 | 0 |
| clean_adm3 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| clean_adm4 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| installer | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| management_clean | 1573 | 0.67 | 5 | 37 | 0 | 7 | 0 |
| status_clean | 0 | 1.00 | 9 | 32 | 0 | 7 | 0 |
| pay | 0 | 1.00 | 2 | 39 | 0 | 7 | 0 |
| fecal_coliform_presence | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| subjective_quality | 0 | 1.00 | 18 | 20 | 0 | 4 | 0 |
| activity_id | 4757 | 0.00 | 36 | 36 | 0 | 3 | 0 |
| scheme_id | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| wpdx_id | 0 | 1.00 | 12 | 12 | 0 | 4760 | 0 |
| notes | 0 | 1.00 | 2 | 96 | 0 | 3502 | 0 |
| orig_lnk | 4757 | 0.00 | 84 | 84 | 0 | 1 | 0 |
| photo_lnk | 41 | 0.99 | 84 | 84 | 0 | 4719 | 0 |
| country_id | 0 | 1.00 | 2 | 2 | 0 | 1 | 0 |
| data_lnk | 0 | 1.00 | 79 | 96 | 0 | 2 | 0 |
| water_point_history | 0 | 1.00 | 142 | 834 | 0 | 4750 | 0 |
| clean_country_id | 0 | 1.00 | 3 | 3 | 0 | 1 | 0 |
| country_name | 0 | 1.00 | 7 | 7 | 0 | 1 | 0 |
| water_source | 0 | 1.00 | 8 | 30 | 0 | 4 | 0 |
| water_tech | 0 | 1.00 | 5 | 37 | 0 | 20 | 0 |
| adm2 | 0 | 1.00 | 3 | 14 | 0 | 33 | 0 |
| adm3 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| management | 1573 | 0.67 | 5 | 47 | 0 | 7 | 0 |
| adm1 | 0 | 1.00 | 4 | 5 | 0 | 4 | 0 |
| New Georeferenced Column | 0 | 1.00 | 16 | 35 | 0 | 4760 | 0 |
| lat_lon_deg | 0 | 1.00 | 13 | 32 | 0 | 4760 | 0 |
| public_data_source | 0 | 1.00 | 84 | 102 | 0 | 2 | 0 |
| converted | 0 | 1.00 | 53 | 53 | 0 | 1 | 0 |
| created_timestamp | 0 | 1.00 | 22 | 22 | 0 | 2 | 0 |
| updated_timestamp | 0 | 1.00 | 22 | 22 | 0 | 2 | 0 |
| Geometry | 0 | 1.00 | 33 | 37 | 0 | 4760 | 0 |
| ADM2_EN | 0 | 1.00 | 3 | 14 | 0 | 30 | 0 |
| ADM2_PCODE | 0 | 1.00 | 8 | 8 | 0 | 30 | 0 |
| ADM1_EN | 0 | 1.00 | 4 | 4 | 0 | 1 | 0 |
| ADM1_PCODE | 0 | 1.00 | 5 | 5 | 0 | 1 | 0 |
Variable type: logical
| skim_variable | n_missing | complete_rate | mean | count |
|---|---|---|---|---|
| rehab_year | 4760 | 0 | NaN | : |
| rehabilitator | 4760 | 0 | NaN | : |
| is_urban | 0 | 1 | 0.39 | FAL: 2884, TRU: 1876 |
| latest_record | 0 | 1 | 1.00 | TRU: 4760 |
| status | 0 | 1 | 0.56 | TRU: 2642, FAL: 2118 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| row_id | 0 | 1.00 | 68550.48 | 10216.94 | 49601.00 | 66874.75 | 68244.50 | 69562.25 | 471319.00 | ▇▁▁▁▁ |
| lat_deg | 0 | 1.00 | 7.68 | 0.22 | 7.06 | 7.51 | 7.71 | 7.88 | 8.06 | ▁▂▇▇▇ |
| lon_deg | 0 | 1.00 | 4.54 | 0.21 | 4.08 | 4.36 | 4.56 | 4.71 | 5.06 | ▃▆▇▇▂ |
| install_year | 1144 | 0.76 | 2008.63 | 6.04 | 1917.00 | 2006.00 | 2010.00 | 2013.00 | 2015.00 | ▁▁▁▁▇ |
| fecal_coliform_value | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| distance_to_primary_road | 0 | 1.00 | 5021.53 | 5648.34 | 0.01 | 719.36 | 2972.78 | 7314.73 | 26909.86 | ▇▂▁▁▁ |
| distance_to_secondary_road | 0 | 1.00 | 3750.47 | 3938.63 | 0.15 | 460.90 | 2554.25 | 5791.94 | 19559.48 | ▇▃▁▁▁ |
| distance_to_tertiary_road | 0 | 1.00 | 1259.28 | 1680.04 | 0.02 | 121.25 | 521.77 | 1834.42 | 10966.27 | ▇▂▁▁▁ |
| distance_to_city | 0 | 1.00 | 16663.99 | 10960.82 | 53.05 | 7930.75 | 15030.41 | 24255.75 | 47934.34 | ▇▇▆▃▁ |
| distance_to_town | 0 | 1.00 | 16726.59 | 12452.65 | 30.00 | 6876.92 | 12204.53 | 27739.46 | 44020.64 | ▇▅▃▃▂ |
| rehab_priority | 2654 | 0.44 | 489.33 | 1658.81 | 0.00 | 7.00 | 91.50 | 376.25 | 29697.00 | ▇▁▁▁▁ |
| water_point_population | 4 | 1.00 | 513.58 | 1458.92 | 0.00 | 14.00 | 119.00 | 433.25 | 29697.00 | ▇▁▁▁▁ |
| local_population_1km | 4 | 1.00 | 2727.16 | 4189.46 | 0.00 | 176.00 | 1032.00 | 3717.00 | 36118.00 | ▇▁▁▁▁ |
| crucialness_score | 798 | 0.83 | 0.26 | 0.28 | 0.00 | 0.07 | 0.15 | 0.35 | 1.00 | ▇▃▁▁▁ |
| pressure_score | 798 | 0.83 | 1.46 | 4.16 | 0.00 | 0.12 | 0.41 | 1.24 | 93.69 | ▇▁▁▁▁ |
| usage_capacity | 0 | 1.00 | 560.74 | 338.46 | 300.00 | 300.00 | 300.00 | 1000.00 | 1000.00 | ▇▁▁▁▅ |
| days_since_report | 0 | 1.00 | 2692.69 | 41.92 | 1483.00 | 2688.00 | 2693.00 | 2700.00 | 4645.00 | ▁▇▁▁▁ |
| staleness_score | 0 | 1.00 | 42.80 | 0.58 | 23.13 | 42.70 | 42.79 | 42.86 | 62.66 | ▁▁▇▁▁ |
| location_id | 0 | 1.00 | 235865.49 | 6657.60 | 23741.00 | 230638.75 | 236199.50 | 240061.25 | 267454.00 | ▁▁▁▁▇ |
| cluster_size | 0 | 1.00 | 1.05 | 0.25 | 1.00 | 1.00 | 1.00 | 1.00 | 4.00 | ▇▁▁▁▁ |
| lat_deg_original | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| lon_deg_original | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| count | 0 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▇▁▁ |
Osun_wp_sf_clean <- Osun_wp_sf %>%
filter_at(vars(status,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
water_point_population,
local_population_1km,
usage_capacity,
is_urban,
water_source_clean),
all_vars(!is.na(.))) %>%
mutate(usage_capacity = as.factor(usage_capacity))The code chunk below is used to drop away geometric column
Osun_wp <- Osun_wp_sf_clean %>%
select(c(7,35:39,42:43,46:47,57)) %>%
st_set_geometry(NULL)cluster_vars.cor = cor(
Osun_wp[,2:7])
corrplot.mixed(cluster_vars.cor,
lower = "ellipse",
upper = "number",
tl.pos = "lt",
diag = "l",
tl.col = "black")
model <- glm(status ~ distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = Osun_wp_sf_clean,
family = binomial(link = "logit"))Instead of using typical R project, blr_regress() of blorr package is used.
blr_regress(model) Model Overview
------------------------------------------------------------------------
Data Set Resp Var Obs. Df. Model Df. Residual Convergence
------------------------------------------------------------------------
data status 4756 4755 4744 TRUE
------------------------------------------------------------------------
Response Summary
--------------------------------------------------------
Outcome Frequency Outcome Frequency
--------------------------------------------------------
0 2114 1 2642
--------------------------------------------------------
Maximum Likelihood Estimates
-----------------------------------------------------------------------------------------------
Parameter DF Estimate Std. Error z value Pr(>|z|)
-----------------------------------------------------------------------------------------------
(Intercept) 1 0.3887 0.1124 3.4588 5e-04
distance_to_primary_road 1 0.0000 0.0000 -0.7153 0.4744
distance_to_secondary_road 1 0.0000 0.0000 -0.5530 0.5802
distance_to_tertiary_road 1 1e-04 0.0000 4.6708 0.0000
distance_to_city 1 0.0000 0.0000 -4.7574 0.0000
distance_to_town 1 0.0000 0.0000 -4.9170 0.0000
water_point_population 1 -5e-04 0.0000 -11.3686 0.0000
local_population_1km 1 3e-04 0.0000 19.2953 0.0000
usage_capacity1000 1 -0.6230 0.0697 -8.9366 0.0000
is_urbanTRUE 1 -0.2971 0.0819 -3.6294 3e-04
water_source_cleanProtected Shallow Well 1 0.5040 0.0857 5.8783 0.0000
water_source_cleanProtected Spring 1 1.2882 0.4388 2.9359 0.0033
-----------------------------------------------------------------------------------------------
Association of Predicted Probabilities and Observed Responses
---------------------------------------------------------------
% Concordant 0.7347 Somers' D 0.4693
% Discordant 0.2653 Gamma 0.4693
% Tied 0.0000 Tau-a 0.2318
Pairs 5585188 c 0.7347
---------------------------------------------------------------report(model)We fitted a logistic model (estimated using ML) to predict status with
distance_to_primary_road (formula: status ~ distance_to_primary_road +
distance_to_secondary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + water_point_population + local_population_1km +
usage_capacity + is_urban + water_source_clean). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
distance_to_primary_road = 0, is at 0.39 (95% CI [0.17, 0.61], p < .001).
Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_secondary_road
(formula: status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_secondary_road = 0,
is at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_tertiary_road (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_tertiary_road = 0,
is at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_city (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_city = 0, is at 0.39
(95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_town (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_town = 0, is at 0.39
(95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with water_point_population (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to water_point_population = 0, is
at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with local_population_1km (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to local_population_1km = 0, is at
0.39 (95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with usage_capacity (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to usage_capacity = 300, is at 0.39
(95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with is_urban (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to is_urban = [?], is at 0.39 (95%
CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation. and We fitted a logistic
model (estimated using ML) to predict status with water_source_clean (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to water_source_clean = Borehole,
is at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
- The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
- The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation.blr_confusion_matrix(model, cutoff = 0.5)Confusion Matrix and Statistics
Reference
Prediction FALSE TRUE
0 1301 738
1 813 1904
Accuracy : 0.6739
No Information Rate : 0.4445
Kappa : 0.3373
McNemars's Test P-Value : 0.0602
Sensitivity : 0.7207
Specificity : 0.6154
Pos Pred Value : 0.7008
Neg Pred Value : 0.6381
Prevalence : 0.5555
Detection Rate : 0.4003
Detection Prevalence : 0.5713
Balanced Accuracy : 0.6680
Precision : 0.7008
Recall : 0.7207
'Positive' Class : 1Osun_wp_sp <- Osun_wp_sf_clean %>%
select(c(status,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
water_point_population,
local_population_1km,
usage_capacity,
is_urban,
water_source_clean)) %>%
as_Spatial()
Osun_wp_spclass : SpatialPointsDataFrame
features : 4756
extent : 182502.4, 290751, 340054.1, 450905.3 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs
variables : 11
names : status, distance_to_primary_road, distance_to_secondary_road, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean
min values : 0, 0.014461356813335, 0.152195902540837, 0.017815121653488, 53.0461399623541, 30.0019777713073, 0, 0, 1000, 0, Borehole
max values : 1, 26909.8616132094, 19559.4793799085, 10966.2705628969, 47934.343603562, 44020.6393368124, 29697, 36118, 300, 1, Protected Spring bw.fixed <- bw.ggwr(status ~
distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = Osun_wp_sp,
family = "binomial",
approach = "AIC",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE)Take a cup of tea and have a break, it will take a few minutes.
-----A kind suggestion from GWmodel development group
Iteration Log-Likelihood:(With bandwidth: 95768.67 )
=========================
0 -2889
1 -2836
2 -2830
3 -2829
4 -2829
5 -2829
Fixed bandwidth: 95768.67 AICc value: 5684.357
Iteration Log-Likelihood:(With bandwidth: 59200.13 )
=========================
0 -2875
1 -2818
2 -2810
3 -2808
4 -2808
5 -2808
Fixed bandwidth: 59200.13 AICc value: 5646.785
Iteration Log-Likelihood:(With bandwidth: 36599.53 )
=========================
0 -2847
1 -2781
2 -2768
3 -2765
4 -2765
5 -2765
6 -2765
Fixed bandwidth: 36599.53 AICc value: 5575.148
Iteration Log-Likelihood:(With bandwidth: 22631.59 )
=========================
0 -2798
1 -2719
2 -2698
3 -2693
4 -2693
5 -2693
6 -2693
Fixed bandwidth: 22631.59 AICc value: 5466.883
Iteration Log-Likelihood:(With bandwidth: 13998.93 )
=========================
0 -2720
1 -2622
2 -2590
3 -2581
4 -2580
5 -2580
6 -2580
7 -2580
Fixed bandwidth: 13998.93 AICc value: 5324.578
Iteration Log-Likelihood:(With bandwidth: 8663.649 )
=========================
0 -2601
1 -2476
2 -2431
3 -2419
4 -2417
5 -2417
6 -2417
7 -2417
Fixed bandwidth: 8663.649 AICc value: 5163.61
Iteration Log-Likelihood:(With bandwidth: 5366.266 )
=========================
0 -2436
1 -2268
2 -2194
3 -2167
4 -2161
5 -2161
6 -2161
7 -2161
8 -2161
9 -2161
Fixed bandwidth: 5366.266 AICc value: 4990.587
Iteration Log-Likelihood:(With bandwidth: 3328.371 )
=========================
0 -2157
1 -1922
2 -1802
3 -1739
4 -1713
5 -1713
Fixed bandwidth: 3328.371 AICc value: 4798.288
Iteration Log-Likelihood:(With bandwidth: 2068.882 )
=========================
0 -1751
1 -1421
2 -1238
3 -1133
4 -1084
5 -1084
Fixed bandwidth: 2068.882 AICc value: 4837.017
Iteration Log-Likelihood:(With bandwidth: 4106.777 )
=========================
0 -2297
1 -2095
2 -1997
3 -1951
4 -1938
5 -1936
6 -1936
7 -1936
8 -1936
Fixed bandwidth: 4106.777 AICc value: 4873.161
Iteration Log-Likelihood:(With bandwidth: 2847.289 )
=========================
0 -2036
1 -1771
2 -1633
3 -1558
4 -1525
5 -1525
Fixed bandwidth: 2847.289 AICc value: 4768.192
Iteration Log-Likelihood:(With bandwidth: 2549.964 )
=========================
0 -1941
1 -1655
2 -1503
3 -1417
4 -1378
5 -1378
Fixed bandwidth: 2549.964 AICc value: 4762.212
Iteration Log-Likelihood:(With bandwidth: 2366.207 )
=========================
0 -1874
1 -1573
2 -1410
3 -1316
4 -1274
5 -1274
Fixed bandwidth: 2366.207 AICc value: 4773.081
Iteration Log-Likelihood:(With bandwidth: 2663.532 )
=========================
0 -1979
1 -1702
2 -1555
3 -1474
4 -1438
5 -1438
Fixed bandwidth: 2663.532 AICc value: 4762.568
Iteration Log-Likelihood:(With bandwidth: 2479.775 )
=========================
0 -1917
1 -1625
2 -1468
3 -1380
4 -1339
5 -1339
Fixed bandwidth: 2479.775 AICc value: 4764.294
Iteration Log-Likelihood:(With bandwidth: 2593.343 )
=========================
0 -1956
1 -1674
2 -1523
3 -1439
4 -1401
5 -1401
Fixed bandwidth: 2593.343 AICc value: 4761.813
Iteration Log-Likelihood:(With bandwidth: 2620.153 )
=========================
0 -1965
1 -1685
2 -1536
3 -1453
4 -1415
5 -1415
Fixed bandwidth: 2620.153 AICc value: 4761.89
Iteration Log-Likelihood:(With bandwidth: 2576.774 )
=========================
0 -1950
1 -1667
2 -1515
3 -1431
4 -1393
5 -1393
Fixed bandwidth: 2576.774 AICc value: 4761.889
Iteration Log-Likelihood:(With bandwidth: 2603.584 )
=========================
0 -1960
1 -1678
2 -1528
3 -1445
4 -1407
5 -1407
Fixed bandwidth: 2603.584 AICc value: 4761.813
Iteration Log-Likelihood:(With bandwidth: 2609.913 )
=========================
0 -1962
1 -1680
2 -1531
3 -1448
4 -1410
5 -1410
Fixed bandwidth: 2609.913 AICc value: 4761.831
Iteration Log-Likelihood:(With bandwidth: 2599.672 )
=========================
0 -1958
1 -1676
2 -1526
3 -1443
4 -1405
5 -1405
Fixed bandwidth: 2599.672 AICc value: 4761.809
Iteration Log-Likelihood:(With bandwidth: 2597.255 )
=========================
0 -1957
1 -1675
2 -1525
3 -1441
4 -1403
5 -1403
Fixed bandwidth: 2597.255 AICc value: 4761.809 bw.fixed[1] 2599.672gwlr.fixed <- ggwr.basic(status ~
distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = Osun_wp_sp,
bw = 2597.255,
family="binomial",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE) Iteration Log-Likelihood
=========================
0 -1957
1 -1675
2 -1525
3 -1441
4 -1403
5 -1403 gwlr.fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2022-12-17 11:42:45
Call:
ggwr.basic(formula = status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity +
is_urban + water_source_clean, data = Osun_wp_sp, bw = 2597.255,
family = "binomial", kernel = "gaussian", adaptive = FALSE,
longlat = FALSE)
Dependent (y) variable: status
Independent variables: distance_to_primary_road distance_to_secondary_road distance_to_tertiary_road distance_to_city distance_to_town water_point_population local_population_1km usage_capacity is_urban water_source_clean
Number of data points: 4756
Used family: binomial
***********************************************************************
* Results of Generalized linear Regression *
***********************************************************************
Call:
NULL
Deviance Residuals:
Min 1Q Median 3Q Max
-124.555 -1.755 1.072 1.742 34.333
Coefficients:
Estimate Std. Error z value Pr(>|z|)
Intercept 3.887e-01 1.124e-01 3.459 0.000543
distance_to_primary_road -4.642e-06 6.490e-06 -0.715 0.474422
distance_to_secondary_road -5.143e-06 9.299e-06 -0.553 0.580230
distance_to_tertiary_road 9.683e-05 2.073e-05 4.671 3.00e-06
distance_to_city -1.686e-05 3.544e-06 -4.757 1.96e-06
distance_to_town -1.480e-05 3.009e-06 -4.917 8.79e-07
water_point_population -5.097e-04 4.484e-05 -11.369 < 2e-16
local_population_1km 3.451e-04 1.788e-05 19.295 < 2e-16
usage_capacity1000 -6.230e-01 6.972e-02 -8.937 < 2e-16
is_urbanTRUE -2.971e-01 8.185e-02 -3.629 0.000284
water_source_cleanProtected Shallow Well 5.040e-01 8.574e-02 5.878 4.14e-09
water_source_cleanProtected Spring 1.288e+00 4.388e-01 2.936 0.003325
Intercept ***
distance_to_primary_road
distance_to_secondary_road
distance_to_tertiary_road ***
distance_to_city ***
distance_to_town ***
water_point_population ***
local_population_1km ***
usage_capacity1000 ***
is_urbanTRUE ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6534.5 on 4755 degrees of freedom
Residual deviance: 5688.0 on 4744 degrees of freedom
AIC: 5712
Number of Fisher Scoring iterations: 5
AICc: 5712.099
Pseudo R-square value: 0.1295351
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 2597.255
Regression points: the same locations as observations are used.
Distance metric: A distance matrix is specified for this model calibration.
************Summary of Generalized GWR coefficient estimates:**********
Min. 1st Qu. Median
Intercept -8.9630e+02 -4.9805e+00 1.7599e+00
distance_to_primary_road -1.9477e-02 -4.8092e-04 3.0174e-05
distance_to_secondary_road -1.5757e-02 -3.7583e-04 1.2438e-04
distance_to_tertiary_road -1.5673e-02 -4.2538e-04 7.6217e-05
distance_to_city -1.8447e-02 -5.6287e-04 -1.2745e-04
distance_to_town -2.2450e-02 -5.7335e-04 -1.5218e-04
water_point_population -5.2830e-02 -2.2810e-03 -9.8829e-04
local_population_1km -1.2757e-01 5.0016e-04 1.0647e-03
usage_capacity1000 -2.0846e+01 -9.7311e-01 -4.1596e-01
is_urbanTRUE -1.9866e+02 -4.3054e+00 -1.6908e+00
water_source_cleanProtected.Shallow.Well -2.0782e+01 -4.5536e-01 5.3278e-01
water_source_cleanProtected.Spring -5.2495e+02 -5.5983e+00 2.5500e+00
3rd Qu. Max.
Intercept 1.2829e+01 1075.4234
distance_to_primary_road 4.8497e-04 0.0143
distance_to_secondary_road 6.0665e-04 0.0259
distance_to_tertiary_road 6.7104e-04 0.0129
distance_to_city 2.3763e-04 0.0155
distance_to_town 1.9318e-04 0.0225
water_point_population 5.0564e-04 0.1313
local_population_1km 1.8177e-03 0.0392
usage_capacity1000 3.0334e-01 5.9492
is_urbanTRUE 1.2864e+00 746.9498
water_source_cleanProtected.Shallow.Well 1.7870e+00 67.5549
water_source_cleanProtected.Spring 6.7736e+00 331.1243
************************Diagnostic information*************************
Number of data points: 4756
GW Deviance: 2792.323
AIC : 4413.603
AICc : 4747.217
Pseudo R-square value: 0.5726785
***********************************************************************
Program stops at: 2022-12-17 11:44:17 Converting SDF into sf data.frame
To assess the performance of the gwLR, firstly, we will convert the SDF object in as data frame by using the code below:
gwr.fixed <- as.data.frame(gwlr.fixed$SDF)Next, we will label yhat values greater or equal to 0.5 into 1 and else 0. In result of the logic comparison operation will be saved into a field called most.
gwr.fixed <- gwr.fixed %>%
mutate(most = ifelse(
gwr.fixed$yhat >= 0.5, T, F))gwr.fixed$y <- as.factor(gwr.fixed$y)
gwr.fixed$most <- as.factor(gwr.fixed$most)
CM <- confusionMatrix(data=gwr.fixed$most, reference = gwr.fixed$y)
CMConfusion Matrix and Statistics
Reference
Prediction FALSE TRUE
FALSE 1824 263
TRUE 290 2379
Accuracy : 0.8837
95% CI : (0.8743, 0.8927)
No Information Rate : 0.5555
P-Value [Acc > NIR] : <2e-16
Kappa : 0.7642
Mcnemar's Test P-Value : 0.2689
Sensitivity : 0.8628
Specificity : 0.9005
Pos Pred Value : 0.8740
Neg Pred Value : 0.8913
Prevalence : 0.4445
Detection Rate : 0.3835
Detection Prevalence : 0.4388
Balanced Accuracy : 0.8816
'Positive' Class : FALSE
Visualising gwLR
Osun_wp_sf_selected <- Osun_wp_sf_clean %>%
select(c(ADM2_EN, ADM2_PCODE,
ADM1_EN, ADM1_PCODE,
status))gwr_sf.fixed <- cbind(Osun_wp_sf_selected, gwr.fixed)The code chunk below is used to create an interactive point symbol map.
tmap_mode("view")tmap mode set to interactive viewingprob_T <- tm_shape(Osun) +
tm_polygons(alpha=0.1) +
tm_shape (gwr_sf.fixed) +
tm_dots(col="yhat",
border.col ="gray60",
border.lwd=1) +
tm_view(set.zoom.limits = c(8,14))
prob_T